Length of the rug is 15 feet and the width of the rug is 3 feet. What is the area of the rug?

Answer:

x = 12

Solve for x:

Using Pythagorean Theorem

a^2 + b^2 = c^2

a = 9

c = 15

b = x

9^2 + x^2 = 15^2

81 + x^2 = 225

x^2 = 144 | sqrt

x = 12

Answer:

81 : 8

Step-by-step explanation:

Cube 1 has side lengths of 3, so it's volume is 3³ = 81

Cube 2 has side lengths of 2, so it's volume is 2³ = 8

So the ration of volume of the larger cube to the smaller cube is 81 : 8

Answer:

A square that has sides of 4.5 units, or a rectangle that is 1 unit wide and 8 units long.

Step-by-step explanation:

First, you need to find the perimeter in the first place. Since there are two sides of the same number, you would double each number.

2 would become 4

6 would become 12

Add 4+12=18

So, our rectangle has to have a perimeter of 18 units. Because a square is a rectangle, you can divide 18 and 4, since a square has 4 sides. You get 4.5. Each side can be 4.5 units.

Or, you can have a rectangle. What I thought first was a length of 9, but I knew that wouldn't work. I drew a rectangle and tried 8. If I put it on the top and bottom, which you need to to find the perimeter, it was only 16. Then I knew I could use 1 as a side length. If you added the sides, it would equal 2, and when you add 16 and 2, it's 18. So, you can use a rectangle that has a length of 8 units and a width of 1 unit.

Answer:

∠P = 65°

Step-by-step explanation:

The measure of arcs LP and PY are given as 80° and 150°, so their sum is 230°. Arc LY completes the circle of 360°, so is 130°. Inscribed angle P is half that measure, so ...

∠P = 130°/2 = 65°.

Final answer:

Toshi has 1 1/4 hours left before he can leave work, which is found by subtracting the time he has already worked (1 3/4 hours) from his total shift (3 hours).

Explanation:

The student asked how many more hours Toshi has to work before he can leave the car wash, given that he has to work a total of 3 hours and has already worked 1 3/4 hours. To find this out, we subtract the time already worked from the total work time required:

Convert 1 3/4 hours to an improper fraction: 1 3/4 = 7/4 hours.

Convert 3 hours to 4/4 hours increments to have a common denominator: 3 hours = 12/4 hours.

Subtract the time worked from the total time: 12/4 - 7/4 = 5/4 hours.

Convert the answer back to mixed numbers: 5/4 hours = 1 1/4 hours.

Therefore, Toshi has 1 1/4 hours left before he can leave work.

i think the answer is B

The value of x2 is 24.

Two variables are inversely varying if one variable value increases then other variable value decreases. We can represent this relation with an equation

y ∝ 1/x

⇒ y=k/x

where k is a constant.

According to asked problem y is varying inversely with x.

given, x1=6

y1=8

putting these values in the above equation,

8=k/6

⇒k=48

Now we have the value of k.

So the inversely varying equation will become,

y=48/x

By putting the value y2=2

2=48/x

⇒x=48/2

⇒x=24

The value of x2 is 24.

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Answer:

The answer in the procedure

Step-by-step explanation:

step 1

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=10\ cm[/tex]

[tex]h=9\ cm[/tex]

substitute

[tex]V=\pi (10)^{2}(9)=900\pi\ cm^{2}[/tex]  

step 2

Find the volume of the cone

The volume of the cone is equal to

[tex]V=(1/3)\pi r^{2} h[/tex]

we have

[tex]r=10\ cm[/tex]

[tex]h=9\ cm[/tex]

substitute

[tex]V=(1/3)\pi (10)^{2}(9)=300\pi\ cm^{2}[/tex]  

therefore

we have

[tex]Vcylinder=900\pi\ cm^{2}[/tex]  

[tex]Vcone=300\pi\ cm^{2}[/tex]  

so

[tex]Vcylinder=3Vcone[/tex]  

Answer:

x < -12

Step-by-step explanation:

-1/2x > 6

Multiply by -2 to isolate x

Remember that when multiplying by a negative, we flip the inequality

-2 * -1/2x < 6*-2

x < -12

Answer:

Each person will have the amount of 4/20 ft piece of gum equivalent to 1/5 ft

Step-by-step explanation:

we know that

For sharing the 1/4 piece of gum equally with 5 people, first divide each piece of 1/4 by 5

so

[tex]\frac{(1/4)}{5}=\frac{1}{20}\ ft[/tex]

At this moment we have 20 pieces and each one is 1/20 ft

The number of pieces that corresponds to each person is 20 divided by 5.

so

[tex]20/5=4[/tex]      

[tex]4*\frac{1}{20}=\frac{4}{20}\ ft[/tex]

each person will have the amount of 4/20 ft piece of gum

simplify

[tex]\frac{4}{20}=\frac{1}{5}\ ft[/tex]

Answer:

each person gets 4/20 pieces

Step-by-step explanation:

(1/4)/5

Answer: [tex]\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}[/tex]

               b) 5314

               c) ln 2.7

               d) 4.6 hrs

Step-by-step explanation:

[tex]P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}[/tex]

[tex]10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}[/tex]

Final answer:

The question involves solving an exponential growth problem, often modeled by the equation P(t) = P0ekt, to determine the bacterial population at specific times and the growth rate after 4 hours, as well as the time it takes to reach a certain population size.

Explanation:

The student's question falls into the realm of differential equations and specifically pertains to exponential growth in the context of a bacteria population. When dealing with bacterial growth, the formula used is P(t) = P0ekt, where P0 is the initial population, e is the base of the natural logarithm, k is the rate constant, and t is the time in hours.

To find the expression for P(t), we first need to determine the value of k using the information that after one hour the population has increased from 100 to 270 cells. We can then use this value to determine P(4), the population after 4 hours, and P'(4), the rate of growth after 4 hours. Finally, to find when the population reaches 10,000 cells we solve P(t) = 10,000.

Here are the steps we follow:

The price increased so it would be a positive net change.

Subtract the new price from the original price:

45.83 - 30.46 = 15.37

The net change was C. $15.37

Answer:

C) 15,37

Step-by-step explanation:

You can to obtain the net change in the stock price with a substract:

Vt = [Pf - Pi]

Vt = [$45.83 - 30.46]

Vt = 15.37

Its a positive variation

Best regards

Answer:

2/5 of the students

Step-by-step explanation:

Let the total number of students be x. Two-Thirds of the students plan to do some volunteering. Two-Thirds in fraction can be written as 2/3. So the portion of the students which plan to do some volunteering is:

[tex]\frac{2x}{3}[/tex]

From these students, 3/5 plan to volunteer at community center. So the students who plan to volunteer at community center will be:

[tex]\frac{2x}{3} \times \frac{3}{5}\\\\  = \frac{2x}{5}[/tex]

This means, among x students, 2/5 of the students plan to volunteer at the community center this summer.

Answer:

The measures would be 30, 60, and 90 degrees.

Step-by-step explanation:

60 is 30 more than 30, and 90 is the sum of 30 and 60. Also the sum of the measures of triangle is always 180, and 30 + 60 + 90 = 180.

If One angle of a triangle is 30 degrees more than the smallest angle. The largest angle is the sum of the other angles. Then 30, 60 and 90 are

measures of all three angles.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

One angle of a triangle is 30 degrees more than the smallest angle.

x=30+y

The largest angle is the sum of the other angles

z=x+y

By angle sum property the sum of three angles is 180 degrees

x+y+z=180

30+y+y+z=180

30+y+y+30+y+y=180

60+4y=180

Subtract 60 from both sides

4y=120

Divide 4 on both sides

y=30

Now substitute y value in x

x=60

z=90

Hence the measure of all three angles are 30,60 and 90 degrees.

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Answer: 6.85

Step-by-step explanation: 4 divided by 5 equals .8, so you need to write any number that is greater than 6.8, but less than 7. Other options would be 6.86, 6.9 or 6.95.

Answer:

Final answer is approx x=-0.66.

Step-by-step explanation:

Given equation is [tex]5^{-2x-1}=4^{4x+3} [/tex].

Now we need to solve equation [tex]5^{-2x-1}=4^{4x+3} [/tex] and round to the nearest hundredth.

[tex]5^{-2x-1}=4^{4x+3} [/tex]

[tex]\log(5^{-2x-1})=\log(4^{4x+3}) [/tex]

[tex](-2x-1)\log(5)=(4x+3)\log(4) [/tex]

[tex]-2x \log(5)- \log(5)=4x \log(4)+3 \log(4) [/tex]

[tex]-2x \log(5) -4x \log(4)=3 \log(4) +\log(5)[/tex]

[tex]x=\frac{\left(3\log(4)+\log(5)\right)}{\left(-2\log(5)-4\log(4)\right)}[/tex]

Now use calculator to calculate log values, we get:

[tex]x=-0.65817959094[/tex]

Round to the nearest hundredth.

Hence final answer is approx x=-0.66.

Answer:

A

Step-by-step explanation:

The statement "If x = 3, then x^2 = 3x" was formed by multiplying x = 3 by x on both sides. Thus x = 3 becomes x*x=3*x. This simplifies to x^2 = 3x. This property is the multiplication property of equality.

The multiplication property of equality is used to arrive at the conclusion from 'x = 3' to 'x^2 = 3x'. This property allows you to multiply both sides of an equation by the same non-zero number, maintaining equality.

The property of equality used to reach the conclusion from 'x = 3' to 'x^2 = 3x' is the multiplication property of equality. This property states that if you multiply both sides of an equation by the same non-zero number, the equation will still be equal. Here, 'x' is being replaced by '3' in 'x^2', leading to '3x'. Therefore, the multiplication property of equality is applied.

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Answer: The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

i.e.  0.2<0.42<0.7<0.87

Step-by-step explanation:

Since we have given that

1) the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles

Probability would be [tex]\dfrac{\text{Red Marble}}{Total\ marble}}=\dfrac{5}{12}=0.42[/tex]

2) the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples

Probability would be [tex]\dfrac{Peach}{Total}=\dfrac{7}{10}=0.7[/tex]

3) the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens

Probability would be [tex]\dfrac{Green}{Total}=\dfrac{4}{20}=\dfrac{1}{5}=0.2[/tex]

4) the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls

Probability would be [tex]\dfrac{Golf\ ball}{Total}=\dfrac{13}{15}=0.87[/tex]

We need to arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability occurrence:

So, 0.2<0.42<0.7<0.87

Hence, it becomes

the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

Answer:

Choice A

Step-by-step explanation:

The scenario presented relates to exponential growth models; the population of bacteria is growing at an exponential rate given by the equation;

[tex]B=1000e^{kt}[/tex]

In this case B represents the population of the bacteria, t the time in minutes, k the growth constant and 1000 represents the initial population at time 0.

After 15 minutes, the population of bacteria grows to 8520. This implies that B is 8520 while t is 15. We substitute this values into the given equation and solve for k, the growth constant;

[tex]8520=1000e^{15k}[/tex]

Divide both sides by 1000;

[tex]8.52=e^{15k}[/tex]

The next step is to introduce natural logs on both sides of the equation;

[tex]ln8.52=ln(e^{15k})\\ln8.52=15k\\k=\frac{ln8.52}{15}=0.143[/tex]

Answer:

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

Answer:

A.

Step-by-step explanation:

I just got 100% on the quiz.

Answer:

A) 0.947; B) 0.0392; C) 0.7257; D) 6th

Step-by-step explanation:

For part A,

We find the z-score for both of these values and subtract them; this will give us the area under the curve between the scores, which is the same as the probability between them.

[tex]z=\frac{X-\mu}{\sigma}\\\\z=\frac{1000-1252}{129}\text{ and } z=\frac{1500-1252}{129}\\\\z=\frac{-252}{129}\text{ and } z=\frac{248}{129}\\\\z=-1.95\text{ and }z=1.92[/tex]

Using a z-table, we see that the area to the right of z = -1.95 is 0.0256.  The area to the right of z = 1.92 is 0.9726.  This means the area between them is

0.9726 - 0.0256 = 0.947.

For part B,

To find the probability that fewer than 1025 chips are in the bag, we find the z-score:

[tex]z=\frac{X-\mu}{\sigma}=\frac{1025-1252}{129}=\frac{-227}{129}\\\\=-1.76[/tex]

Looking this number up in the z-table, we find the area under the curve to the left of, or less than, this is 0.0392.

For part C,

Once we find the z-score for the value 1175, the z-table chart will give us the area under the curve less than this.  To find the proportion greater than this, we subtract from 1:

[tex]z=\frac{X-\mu}{\sigma}=\frac{1175-1252}{129}=\frac{-77}{129}=-0.60[/tex]

In the z-table, we see that the area under the curve less than this is 0.2743.  This means that the area greater than this is 1-0.2743 = 0.7257.

For part D,

We again find the area under the curve less than this.  This tells us the proportion of values that will be less than this; this will tell us the percentile value for this.

[tex]z=\frac{1050-1252}{129}=\frac{-202}{129}=-1.57[/tex]

In the z-table, we see the area to the right of this is 0.0582.  This means that 5.82% of values are less than this; this means the value is the 5.82 percentile, which rounds to the 6th percentile.

These questions are solved by converting the specified number of chips to a Z-score and using it to find the corresponding probability in a standard normal distribution table. The various calculated probabilities provide the answers to the different parts of the question.

In order to answer these questions, we need to convert the number of chips to a Z-score, which is a measure of how many standard deviations an element is from the mean, and then find the corresponding probability from a standard normal distribution table.

(a) To calculate the probability of a bag containing between 1000 - 1500 chips, you subtract the mean from each and divide by the standard deviation to get Z-scores. Then one can find the corresponding probabilities in a Z-table and subtracting the smaller probability from the larger. This will give you the probability of number of chips falling between those two amounts.

(b) Similarly, to compute the probability of a bag containing fewer than 1025 chips, find the Z-score for 1025 and look it up in the Z-table. The probability that corresponds to that Z-score is the likelihood of having fewer than 1025 chips.

(c) For the the proportion of bags that contains more than 1175 chips, first compute the Z-score for 1175. The corresponding probability in the Z-table gives the proportion for those with numbers equal or less than 1175. To get the proportion for bags with more than 1175 chips, you need to subtract that value from 1 (since the total probability is always 1).

(d) Finally, for the percentile rank, it's again the same process. You find the Z-score for 1050, look up its corresponding probability and multiply it by 100 to convert it into percentile rank.

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Answer:

[tex]\boxed{0.2}[/tex]

Step-by-step explanation:

Put -2 where x is in the function and do the arithmetic. Any number of calculators will compute this for you.

  x ≈ 0.23781036584 ≈ 0.2

_____

Comment on the above result

The number above came from the Google calculator (2nd attachment). Surprisingly, it is rounded incorrectly in the last displayed digit. To 20 significant digits, the value is ...

  0.23781036584658190876

It appears the Google calculator didn't carry enough digits to get the answer correct in the last displayed decimal place.

Answer:

your answer would be 0.2

Step-by-step explanation:

Answer:

a ∆ABC and ∆EDC are similar

b. AB = 83.3 ft

Step-by-step explanation:

a.  We need to determine if  ∆ABC and ∆EDC are similar.

We know B = D = 90

We know C = C because they are vertical angles and vertical angles are equal

Therefore A = E because they are triangles, and if 2 angles in a triangle are equal the third angles must be equal.

∆ABC and ∆EDC are similar

b.  We know that because they are similar triangles

AB      BC

------ = ---------

ED        DC

Substituting in

AB       62

------ = ---------

125        93

Using cross products

93 AB = 62*125

93 AB = 7750

Divide by 93

AB = 7750/93

AB = 83.3333333333(repeating)

Rounding to the nearest tenth ft

AB = 83.3 ft

Answer:

13.43

Step-by-step explanation:

Law of Sines

x/sin50 = 12/sin42

solve for x and don't forget to put calculator into degree mode

Answer:

[tex]AB\approx13.7cm[/tex] to the nearest  tenth.

Step-by-step explanation:

We know two angles and a given side, we can use the sine rule to find the required length.

[tex]\frac{AB}{\sin(50\degree)}=\frac{12}{\sin(42\degree)}[/tex]

We solve for the AB by multiplying both sides by [tex]\sin(50\degree)[/tex].

This implies that;

[tex]AB=\frac{12}{\sin(42\degree)}\times \sin(50\degree)[/tex]

[tex]AB=13.738[/tex]

[tex]AB\approx13.7cm[/tex] to the nearest  tenth.

Answer:

On the surface of the sea

Step-by-step explanation:

Six feet below sea level is marked as -6

Go up 6 feet

-6+6 =0 feet below sea level

That would mean we are at 0, which would be sea level

We would be on the surface of the sea

Answer:

Step-by-step explanation:

see attached

➷ cos41 = x/55

x = cos41 x 55

x = 41.50902

The correct option would be 41.51

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Answer:

41.51

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{55}[/tex]

Multiply both sides by 55

55 × cos41° = x

⇒ x = 41.51 ( to the nearest hundredth )

The first one is 4/9 and the second one is 5/9

Final answer:

The probability that the first horse selected is tan and the second horse selected is brown, out of a total of 5 brown horses and 4 tan horses, is 5/18.

Explanation:

The question asks for the probability that the first horse selected is tan, and the second horse selected is brown when there are 5 brown horses and 4 tan horses in a barn. To find this probability, we will multiply the probability of each event happening in sequence.

First, the probability of selecting a tan horse out of the total 9 horses (5 brown + 4 tan) is 4/9. Once a tan horse is selected, there are now 8 horses left, 5 of which are brown. Therefore, the probability of then selecting a brown horse is 5/8.

To find the total probability of both events occurring in sequence (first selecting a tan horse, then a brown horse), we multiply the two probabilities together: 4/9 * 5/8 = 20/72, which simplifies to 5/18.

Answer:

D 12½%

Step-by-step explanation:

∆=1.5/2-2/3

=4.5/6-4/6

=0.5/6

∆=0.083 $/lb

X=∆/(original price)•100

=0.083/(2/3)•100

=0.1245•100

X=12.45%

Answer:

b. [tex]\frac{40}{3}[/tex]

Step-by-step explanation:

The given geometric series is;

[tex]20-10+5-\frac{5}{2}+...[/tex]

The first term of this series is

[tex]a_1=20[/tex]

The common ratio is

[tex]r=\frac{-10}{20}=-\frac{1}{2}[/tex]

The sum to infinity of this series is

[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]

Substitute the given values to obtain;

[tex]S_{\infty}=\frac{20}{1--\frac{1}{2}}[/tex]

This implies that;

[tex]S_{\infty}=\frac{20}{\frac{3}{2}}[/tex]

[tex]S_{\infty}=\frac{40}{3}[/tex]

Answer:

B edge

Step-by-step explanation: